Simplify square root of a square root of a^3

$\sqrt{a} \sqrt{a^{3}}$

Step 1

Factor out $a^{2}$ .

$\sqrt{a} \sqrt{a^{2} a}$

Step 2

Pull terms out from under the radical.

$\sqrt{a} (a \sqrt{a})$

Step 3

Multiply $\sqrt{a} (a \sqrt{a})$ .

Raise $\sqrt{a}$ to the power of $1$ .

$a ({\sqrt{a}}^{1} \sqrt{a})$

Raise $\sqrt{a}$ to the power of $1$ .

$a ({\sqrt{a}}^{1} {\sqrt{a}}^{1})$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$a {\sqrt{a}}^{1 + 1}$

Add $1$ and $1$ .

$a {\sqrt{a}}^{2}$

Step 4

Rewrite ${\sqrt{a}}^{2}$ as $a$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{a}$ as $a^{\frac{1}{2}}$ .

$a {(a^{\frac{1}{2}})}^{2}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$a \cdot a^{\frac{1}{2} \cdot 2}$

Combine $\frac{1}{2}$ and $2$ .

$a \cdot a^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$a \cdot a^{\frac{2}{2}}$

Rewrite the expression.

$a \cdot a^{1}$

Simplify.

$a \cdot a$

Step 5

Multiply $a$ by $a$ .

$a^{2}$